Multi-player mathematical games can potentially be very useful modeling tools in concurrent design. The purpose of this paper is to illustrate a variety of concurrent decision-making models that arise in two simple applications where explicit models can be obtained to represent the typical stages of design and manufacturing in product development. The resulting models are bilevel formulations and have the interpretation of a Stackelberg game between two players. The solutions in these models show that while a rich class of concurrent designs are obtained, such bilevel models also lead to different types of singularities in their solution sets.

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